Two Properties Of Maximal Antichains In Strict Chain Product Posets

We present two results on maximal antichains in the strict chain product poset [t(1) + 1] x [t(2) + 1] x ... x [t(n) + 1]. First, we prove that these maximal antichains are also maximum. Second, we prove that there is a bijection between maximal antichains in the strict chain product poset [t(1) + 1] x [t(2) + 1] x ... x [t(n) + 1] and antichains in the nonstrict chain product poset [t(1)] x [t(2)] x ... x [t(n)].